At the beginning of each quarterly period during the fiscal year, and more often if required by the council, the manager shall submit to the council data showing the relation between the estimated and actual revenues and expenditures to date. If it shall appear that the revenues are less than anticipated, the council may reduce the appropriations, as prescribed in §6-35-308, except amounts required for debt and interest charges, and with the further exception that reductions in school appropriation shall be as to total amount only, to such a degree as may be necessary to keep expenditures within the receipts. The manager may provide for monthly or quarterly allotments of appropriations to all departments, agencies or activities within the manager's jurisdiction under such rules as the manager shall prescribe, and make transfers between departments, agencies, or activities within each fund, and when authorized by the city council, from one (1) fund to another; provided, that any transfer of moneys from the city school fund to any other fund shall be made only with the concurrence of the board of education.